Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections

Details Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections Identities in law between quadratic functionals of bivariate Gaussian processes, through Fubini theorems and symmetric projections

2005-01-28

arxiv.org/abs/math/0501506v1

Mathematics

Probability

Scientific paper

We present three new identities in law for quadratic functionals of conditioned bivariate Gaussian processes. In particular, our results provide a two-parameter generalization of a celebrated identity in law, involving the path variance of a Brownian bridge, due to Watson (1961). The proof is based on ideas from a recent note by J. R. Pycke (2005) and on the stochastic Fubini theorem for general Gaussian measures proved in Deheuvels et al. (2004).

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